Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C11⋊#2104 |
| Sylow | C11 ⋊ #2104 |
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|a^2=def,b^2=de,c^2=d,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,f^b=fg,e^c=eg,h^c=h^10133 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2104, C2×C11⋊#2104, #14784762, … |
| maximal normal subgroup of | D11×#2104, C2×C11⋊#2104, #14784762, … |
| maximal quotient of | #14658914, #14658915, #14658916, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6094);